Input optimization: I. Optimal realizations of mathematical models

Mathematical models are considered as input-output systems. The input is data (technological coefficients, available energy, prices) and the output is the feasible set, the set of optimal solutions, and the optimal value. We study when output is a continuous function of input and identify optimal (minimal) realizations of mathematical models. These are states of the model having the property that every stable perturbation of input results in a locally worse (higher) value of the optimal value function. In input optimization we “optimize” mathematical model rather than a specific mathematical program. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by the Gouvernement du Québec, programme de formation de chercheurs et d’action concertée.